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Alvaro.Castro.Castilla@gmail.com

**building a "hybrid" and dynamic mathematical space**

Hello,

Maybe I'm going to say very stupid or crazy thing for real

mathematicians (I'm an architect):

I want to build a concept that I call "dynamic abstract space" ("das"

from now) for a digital architecture project. I would like to be able

to say the idea I have in mind with mathematics.

This is the essence of the idea:

1) I have a n-dimensional space (the "das") which is built from gluing

together ANY number of ANY type of spaces:

A boolea algebra, a Minkowski space, a ring, R=B3, N, C...

2) Then I introduce particles in my space which are m-dimensional

spaces. If the particles are cointained in the space, then there is no

dynamic reconfiguration of the space, but if the particles are not

contained, the space grows until is able to contain them (for example

in a R=B2 space if we want to insert a R=B3 particle, we have to expand

the space up to R=B3, in a very simple situation). That is the reason I

call it "dynamic".

How to mathematically define that space and that particles?

What do you think of explaining programmable objects and their

variables through this "spaces" and "particles"?

-----

The second thing I would ask is:

Is it correct to say that inside a computer simulation we are inside a

mathematical space of, for example:

R=B3 * R+

for a 3-d space running in a continuous time, or:

R=B3 * N

for a 3-d space running in a step by step basis.

?

THANKS for all your help!

:-)